38 Circuit design
I Reactive output
parasitics Γin,main
OMN RE
ΓE
Resistance seen by the intrinsic node should be Ro pt(or 2Ro pt in back-off). After the simulation done in previous section the parasitics of the main and aux are different .Also in the first evaluation will neglect the resistive parasitics which are very small and can be neglected.
For the Auxiliary device the matching network should transfer the load resistance(modulated ) into Ro pt in saturation .
While for the main device another problem arises,the matching can be when the resistance of the load seen after Q.W.T is 2Ro pt in back-off or Ro pt in saturation to respectively the same resistance at the intrinsic drain node .To achieve the matching at both points an offset line should be added.
In the main device case we want a certain OMN that together with the parasitics can transform a resitance RE into the wanted intrinsic resitance Zin,main= RA. But at the same time if RE is changed by a factor α (αRE) even the Zin,main= αRA.The reflection coefficient at intrinsic node:
Γin,main= Zin,main− RA
Zin,main+ RA = S11− ∆sΓE 1 − S22ΓE Offset line
I Reactive
output parasitics Γin,main
OMN
θm
RE ΓE
40 Circuit design
Considering the S matrix of the Reactive parasitics in cascade with OMN the input reflection can be calulcate as follows :
Γin,main= ej∠S21ΓE|RE ,0
Where ΓE|RE ,0is the reflection coefficient seen by the resistance and with impedance reference equal to RE,0.So the reflection coefficient at drain is equal to the reflection coefficient at load with a difference of phase .So if Γin,main=0 even ΓE|RE ,0=0 and viceversa . But if ΓE|RE ,0 different from 0 when the load RE is changed to a value RE = αRE,0the reflection coefficient is different from 0 but since there is the phase difference the input resistance seen by drain is not multiplicated by α.
To achieve the transformation with the same factor an offset line is needed with characteristic impedance RE,0 [R. Quaglia and Ramella (????)].The new network formed by the three circuits in cascade (parasitics ,OMN ,offset line) we call it ˜Sand the transmission coefficient phase now becomes :
∠ ˜S12= ∠S12− θM
where θM is the degree length of the offset line in centerband. The relation of the two reflection coefficients becomes :
Γin,main= ej∠ ˜S21ΓE|RE ,0= ej∠S21−θMΓE|RE ,0
If we set electrical lenght of the offset line equal to the phase of S21plus n times π
θM = ∠S21+ nπ
the modulation of the resistance RE will be reported with the same factor at the input . Zin,main
RA = RE RE,0
For the design of main OMN we consider as the resistance RE,0the resistance of the load transformed by the Q.W.T.Load resistance seen by main is either Ro pt/2 or Ro pt in saturation due to the modulation by Auxiliary . After the transformation by Q.W.T with characteristic impedance Ro pt the resistance seen by the OMN is 2Ro pt or Ro pt respectively.In the center band frequency is not relevant having an offset line characteristic impedance Zo f f set= Ro pt or Zo f f set= 2Ro pt .What changes is the bandwidth of matching in back-off or in saturation depending in our choice os Zo f f set.In other words if Zo f f set= 2Ro pt the band will be wider in back off then in saturation where in saturation will be a impedance step of the load (Ro pt) and the transmission line (Zo f f set) while in back-off load and transmission line resistance is
equal so we obtain a larger bandwidth .The contrary happens if Zo f f set= Ro pt.
In conclusion ,if we want larger bandwidth in back-off characteristic impedance of offset line Zo f f set= 2Ro ptotherwise if we design for larger bandwidth in saturation then Zo f f set= Ro pt.
42 Circuit design
Auxiliary offset line
Similiar considerations are done for the auxiliary offset line .The problem for the auxiliary rises when it is turned off.In this region the intrinsic drain of auxiliary behaves as open an without an offset line the open is not correctly reproduces in output .So the main sees a load resistance in parallel with reactive elements of auxiliary (parasitics and aux OMN).
ΓOU T,P|
ΓG=1 = ej2(∠S1(2P)−θP) where ΓOU T,P|
ΓG=1 is the output reflection coefficient of auxiliary when the intrinsic drain is an open .we can obtain ΓOU T,P=1 if we add a transmission line at the output of auxiliary with characteristic impedance ZP,o f f set = Ro pt and electrical length :
θp= ∠S1 ( 2
P)+ nπ
Auxiliary OMN
The matching circuits OMN for the auxiliary should transform the modulated load resistance Ro pt to the same value at the intrinsic drain .Aux OMN is designed only to match in saturation because it is turned off in the Low Power region .
Main OMN
In difference from Aux OMN the main matching network can be designed in different ways . As demonstrated previously for the offset line and even OMN can be designed to obtain the maximum bandwidth in back-off saturation or an intermediate point .This choice depends on the specifics that the designer has planned .
Fig. 3.10 Output matching optimized in saturation
Fig. 3.11 Output matching optimized in back off
OMN Design solution The goal of the matching network in a power amplifier design is not only to obtain the optimum load at the intrinsic point at center frequency but also to obtain larger bandwidth possible. There is a formula to according to which we can get the best solution for the optimum network in order to obtain maximum flat and the lowest reflection coefficient in the design frequency band given by Doherty (1936).The design will be explained in detalis in section ?? .This circuit will be the reference point for OMN design bandwidth.
OMN embedded parasitics My design of the output matching network uses the output parasitics of the devices (aux and main) to implement a quarter wave transmission line . In lumped element a quarter wave transformer can be implemented as a π-network of 2 shunt capacitors and a series inductance .(see figure)
CDS1.3pF
LD0.66nH Lseries 0.66nH
Cshunt 1.3pF
A Q.W.T in lumped element is implemented if the impedance of the capacitance and inductance are equal in the center frequency.In order to obtain this behaviour it is needed to add an inductance in series to the parasitic inductance 1
ωCDS = ω(LD+ Lseries)
The characteristic impedance of Q.W.T is equal to absolute impedance value of each of lumped elements Z∞=ωC1 =ωL .In this project the center frequency is f0= 3.5GHz ,CDS=
44 Circuit design
1.3pF,LD= 0.66nH for main device.
Z∞= 1
2π f0CDS = 1
2 ∗ π ∗ 3.5GHz ∗ 1.3pF ≈ 34.98Ω
The matching network has to transform the resistance Ro pt to 2Ro pt and∠ ˜S21= nπ.The final load in which the power will be transferred is usually the load that models the antenna with value 50Ω.
It is needed to make the transformation from 50Ω to 50Ω and while a Q.W.T of 34.98Ω is already present ,at the same time having a inverting network so∠ ˜S21= nπ a minimum of 3 Q.W.T including the embedded transformer.Now the resistance should be transformed from 50Ω to Z50∞2=24.47Ω with two quarter wave transformers.
An optimum dual frequency transformer for broader band can be obtained according to paper [Monzon (2003)]. The values of the 2 transmission line impedance are :
Z1= s
Z0
2α(RL− Z0) + r
[Z0
2α(RL− Z0)]2+ Z03RL
Z2= Z0RL Z1
Where Z0= Zin=24.47Ω ,RL= 50Ω,α = (tan(β1l1))2,β1l1electrical length of the first Q.W.T .
CDS1.3pF
LD0.66nH Lseries
Cshunt 1.3pF
Z∞1 Z∞2
50Ω
The final goal is to design the matching networks in distributed elements.So we have to transform the lumped elements to transmission line.The shunt capacitance can is equivalent at certain frequency to a stub transmission line connected in open.The stub impedance at center frequency is :
Z= − jZ0cot(β l) = 1 jωCshunt
In the formula there are two degrees of formula :electrical length and characteristic impedance.I choose electrical length β l=30◦in order that this stub will become short for the third har-monic.
On the other hand the series inductance (with a relatively small value ) can me modelled with a series transmission line that at the same time serves as a connection line for the device (later on the layout).With some tunning of these 2 parameters and optimization can arrive at the same matching as lumped element OMN.
CDS1.3pF
LD0.66nH Z∞series
Z∞stub
Z∞1 Z∞2
50Ω
Fig. 3.12 OMN reflection coefficient in back off and saturation
46 Circuit design
Auxiliary OMN The idea of Auxiliary Output matching network is the same as that of the main OMN but with the difference that here we need an odd number of transformers because it should not be a inverting circuits (when aux is off the open in intrinisc drain is transformed in open at the ouput ). So except for the first transformer we have t add another Q.W.T to match the saturation load impedance seen by aux (100Ω) to the optimal resistance (25Ω) the circuit in distributed element is:
CDS1.3pF
LD0.85nH Z∞series
Z∞stub Z∞1
50Ω
Fig. 3.13 Aux OMN reflection coefficient in saturation